Abstract: The principal resonance of a Duffing oscillator to combined deterministic and narrow band random parametric excitations is investigated. In particular, the case in which the parametric terms sharing close frequencies is examined. For the first time, the method of multiple scales is used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response are studied by means of qualitative analyses. Jumps are shown to occur if the random excita...